Phase-space distance between stationary states modulates phenotypic plasticity in breast cancer

Phenotypic plasticity in breast cancer involves stochastic transitions between gene-expression states associated with clinically distinct subtypes, such as HER2+ and triple-negative breast cancer (TNBC). In non-conservative gene regulatory networks, however, the dynamical features controlling transition probabilities and timescales cannot be consistently reduced to potential-barrier depth, since potential functions are generally non-unique outside equilibrium. Here, by analyzing an NF-κB -centered regulatory network that supports HER2+ and TNBC attractors, we identify a geometric control principle: the phase-space distance between stationary states, together with the bifurcation structure organizing multistability, provides a robust determinant of transition probabilities, times, and variability. We show that multistability is necessary but not sufficient for transitions, whose accessibility is constrained by the global arrangement of basins and the intervening unstable state. Within this framework, we find a marked asymmetry in dynamical sensitivity: the HER2+ regime is robust to intrinsic parameter variations, whereas the TNBC regime strongly amplifies such variations, offering a dynamical explanation for the pronounced gene molecular and clinical variability observed in TNBC. Together, our results establish a general geometric perspective on phenotypic transitions in non-conservative regulatory networks.